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A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem

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Author Info

  • John W. Mamer

    ()
    (Anderson Graduate School of Management, University of California, Los Angeles, Box 951481, 110 Westwood Plaza, Los Angeles, California 90095-1481)

  • Richard D. McBride

    ()
    (Marshall School of Business, University of Southern California, Los Angeles, California 90089-0809)

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    Abstract

    We propose and test a new pricing procedure for solving large-scale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the procedure is the reduction of the number of pivots needed to solve the problem. Our approach is motivated by the column-generation approach of Dantzig-Wolfe decomposition. We test our procedure on two sets of multicommodity flow problems. One group of test problems arises in routing telecommunications traffic and the second group is a set of logistics problem which have been widely used to test multicommodity flow algorithms.

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    File URL: http://dx.doi.org/10.1287/mnsc.46.5.693.12042
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 46 (2000)
    Issue (Month): 5 (May)
    Pages: 693-709

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    Handle: RePEc:inm:ormnsc:v:46:y:2000:i:5:p:693-709

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    Related research

    Keywords: linear programming; multicommodity flows; optimization;

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    Cited by:
    1. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.
    2. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.

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